A conventional phase detecting circuit is explained below. FIG. 30 shows a structure of the conventional phase detecting circuit disclosed in Japanese Patent Application Laid-open No. 6-77737. The conventional phase detecting circuit detects a received signal from a base band signal. In FIG. 30, a reference numeral 101 denotes a quadrant deciding section, 102 denotes a rotation projector, 103 denotes an integrator, 104 denotes a one-bit quantizer, 105 denotes a delay device, 106 denotes an adder, and 107 denotes a low-pass filter. In the conventional example, the rotation projector 102, the integrator 103, the one-bit quantizer 104, the delay device 105, the adder 106, and the quadrant deciding section 101 constitute a delta sigma modulator.
The operation of the conventional phase detecting circuit is explained. The quadrant deciding section 101 decides the quadrant to which the received signal belongs based on a positive or negative sign of the in-phase component and the quadrature component of the received baseband signal, and outputs a coarse phase value corresponding to the result of the decision. When the quadrants of the received signals are in the first, the second, the third, and the fourth quadrants, the quadrant deciding section 101 outputs 0, 1, 2, and 3 respectively.
The rotation projector 102 rotates the reception complex base band signal by +π/4 or −π/4 corresponding to the data output from the delay device 105. The rotation projector 102 outputs a signed value of the rotated signal projected to a straight line that intersects orthogonally at the origin with a straight line that bisects the quadrant detected by the rotation projector 101.
The integrator 103 integrates the output from the rotation projector 102, and the one-bit quantizer 104 quantizes the integrated value. The one-bit quantizer 104 outputs 1 when the output from the integrator 103 is positive, and outputs 0 when this output is negative. The adder 106 adds this output value and the coarse phase value output from the quadrant deciding section 101. The delay device 105 delays the output from the one-bit quantizer 104 by one basic clock (i.e., one cycle) of the delta sigma modulator, and outputs the delayed signal to the rotation projector 102.
The low-pass filter 107 smoothes the quantization noise based on the phase data added. FIG. 31 shows a structure of the low-pass filter 107. In FIG. 31, a reference numeral 201 denotes shift registers, 202-1, 202-2, . . . , and 202-k denote multipliers, and 203 denotes an adder. In the low-pass filter 107, the shift registers 201 sequentially receive the inputs of phase data output from the adder 106. Each of the multipliers 202-1, . . . , and 202-k multiplies the contents of each register with a coefficient, and the adder 203 adds all the multiplied results. For example, when the coefficient is 1/k, a moving average of K sequential stages appears as the output from the adder 203.
The operation of the rotation projector 102 is explained. In the following explanation, the reception complex base band signal is explained as I+jQ. For example, when the output from the delay device 105 is 1, the rotation projector 102 rotates the received signal by −π/4, and it is possible to express the received signal as shown by the equation (1).(I+jQ)(cos(π/4)−j sin(π/4))=((I+Q)+j(−I+Q))/√{square root over (2)}  (1)
On the other hand, when the output from the delay device 105 is 0, the rotation projector 102 rotates the received signal by +π/4, and it is possible to express the received signal as shown by the equation (2).(I+jQ)(cos(π/4)+j sin(π/4))=((I−Q)+j(I+Q))/√{square root over (2)}  (2)
Next, the rotation projector 102 projects this signal to a straight line that intersects orthogonally at the origin with a straight line that bisects the quadrant detected by the quadrant deciding section 101. The direction of the straight line orthogonal with the bisector is determined such that the phase increasing direction in the quadrant detected by the quadrant deciding section 101 coincides with the positive direction of the straight line.
For example, when the received signal is in the first quadrant, the unit direction vector of the straight line that intersects orthogonally at the origin with the straight line that bisects the first quadrant becomes (−1/√2, 1/√2), when the second quadrant side is determined as positive. The projection of the rotated received signal to this straight line is expressed as the inner product of the vector with the unit direction vector of the straight line. Therefore, when the output from the delay device 105 is 1, it is possible to express the projection as shown by the equation (3), and when the output from the delay device 105 is 0, it is possible to express the projection as shown by the equation (4).((I+Q)/√{square root over (2)},(−I+Q)/√{square root over (2)})·(−1/√{square root over (2)}1/√{square root over (2)})=−I  (3)((I−Q)/√{square root over (2)}, (I+Q)/√{square root over (2)})·(−1/√{square root over (2)}, 1/√{square root over (2)})=Q   (4)
Similarly, when the received signal is in the second quadrant, the unit direction vector of the straight line that intersects orthogonally with the straight line that bisects the second quadrant becomes (−1/√2, −1/√2), when the third quadrant side is determined as positive. Therefore, when the output from the delay device 105 is 1, it is possible to express the projection of the rotated received signal to this straight line as shown by the equation (5). When the output from the delay device 105 is 0, it is possible to express the projection as shown by the equation (6).((I+Q)/√{square root over (2)},(−I+Q)/√{square root over (2)})·(−1/√{square root over (2)},−1/√{square root over (2)})=−Q  (5)((I−Q)/√{square root over (2)}(I+Q)/√{square root over (2)})·(−1/√{square root over (2)},−1/√{square root over (2)})=−I  (6)
Similarly, when the received signal is in the third quadrant, the unit direction vector of the straight line that intersects orthogonally with the straight line that bisects the third quadrant becomes (1/√2, −1/√2), when the fourth quadrant side is determined as positive. Therefore, when the output from the delay device 105 is 1, it is possible to express the projection of the rotated received signal to this straight line as shown by the equation (7). When the output from the delay device 105 is 0, it is possible to express the projection as shown by the equation (8).((I+Q)/√{square root over (2)},(−I+Q)/√{square root over (2)})·(1/√{square root over (2)},−1/√{square root over (2)})=I  (7)((I−Q)/√{square root over (2)},(I+Q)/{square root over (2)})·(1/√{square root over (2)},−1/√{square root over (2)})=−Q   (8)
Similarly, when the received signal is in the fourth quadrant, the unit direction vector of the straight line that intersects orthogonally with the straight line that bisects the fourth quadrant becomes (1/√2, 1/√2), when the first quadrant side is determined as positive. Therefore, when the output from the delay device 105 is 1, it is possible to express the projection of the rotated received signal to this straight line as shown by the equation (9). When the output from the delay device 105 is 0, it is possible to express the projection as shown by the equation (10).((I+Q)/√{square root over (2)},(−I+Q)/√{square root over (2)})·(1/√{square root over (2)},1/√{square root over (2)})=Q   (9)((I−Q)/√{square root over (2)},(I+Q)/√{square root over (2)})·(1/√{square root over (2)},1/√{square root over (2)})=I  (10)
In other words, the rotation projector 102 selectively outputs:    (1) −I, when the received signal is in the first quadrant, and also when the output from the delay device 105 is 1,    (2) Q, when the received signal is in the first quadrant, and also when the output from the delay device 105 is 0,    (3) −Q, when the received signal is in the second quadrant, and also when the output from the delay device 105 is 1,    (4) −I, when the received signal is in the second quadrant, and also when the output from the delay device 105 is 0,    (5) I, when the received signal is in the third quadrant, and also when the output from the delay device 105 is 1,    (6) −Q, when the received signal is in the third quadrant, and also when the output from the delay device 105 is 0,    (7) Q, when the received signal is in the fourth quadrant, and also when the output from the delay device 105 is 1, and    (8) I, when the received signal is in the fourth quadrant, and also when the output from the delay device 105 is 0.
The output from the adder 106 is the sum of the coarse phase value output from the quadrant deciding section 101 and the output from the one-bit quantizer 104. Therefore, the output from the adder 106 becomes:    (1) 1, when the received signal is in the first quadrant, and also when the output from the integrator 103 is positive,    (2) 0, when the received signal is in the first quadrant, and also when the output from the integrator 103 is negative,    (3) 2, when the received signal is in the second quadrant, and also when the output from the integrator 103 is positive,    (4) 1, when the received signal is in the second quadrant, and also when the output from the integrator 103 is negative,    (5) 3, when the received signal is in the third quadrant, and also when the output from the integrator 103 is positive,    (6) 2, when the received signal is in the third quadrant, and also when the output from the integrator 103 is negative,    (7) 4, when the received signal is in the fourth quadrant, and also when the output from the integrator 103 is positive, and    (8) 3, when the received signal is in the fourth quadrant, and also when the output from the integrator 103 is negative.
In summary, it is possible to express the outputs from the quadrant deciding section 101, the rotation projector 102, and the one-bit quantizer 104 respectively as shown in FIG. 32.
The method of detecting the phase of the received baseband signal is explained based on an example that the reception complex base band signal A exp(jθ) (=I+jQ) is in the first quadrant. I=A cos θ, and Q=A sin θ.
First, the rotation projector 102 outputs −I or Q to the integrator 103 based on the output from the delay device 105. The integrator 103 integrates the output from the rotation projector 102. The output from the integrator 103 shows the average of the outputs from the rotation projector 102. The one-bit quantizer 104 decides whether the output from the integrator is positive or negative. When the output from the integrator 103 is positive, the one-bit quantizer 104 outputs 1, and at the same time, makes the rotation projector 102 output −I via the delay device 105. When the output from the integrator 103 is negative, the one-bit quantizer 104 outputs 0, and at the same time, makes the rotation projector 102 output Q via the delay device 105. Based on the work of the feedback loop, the output from the integrator 103, that is, the output from the rotation projector 102, is controlled to approach to zero.
The delta sigma modulator (corresponding to the quadrant deciding section 101, the rotation projector 102, the integrator 103, the one-bit quantizer 104, the delay device 105, and the adder 106) is operated by N cycles (where N is a natural number). During this period, when the one-bit quantizer 104 outputs positive values by p times and outputs negative values by q times, “−pI+qQ≈0” and “p+q=N” are established as a result of the feedback control, when N is sufficiently large. As the adder 106 outputs 1 by p times and outputs 0 by q times, the low-pass filter 107 obtains a simple average of the outputs from the adder 106. It is possible to express the output from the low-pass filter 107 as shown by the equation (11).(1·p+0·q)/N=Q/(I+Q)=tan θ/(1+tan θ)  (11)
Therefore, the output from the low-pass filter 107 becomes    (1) tan θ/(1+tan θ)=0, when θ=0,    (2) tan θ/(1+tan θ)=0.366≈⅓, when θ=π/6,    (3) tan θ/(1+tan θ)=½, when θ=π/4,    (4) tan θ/(1+tan θ)=0.634≈⅔, when θ=π/3, and    (5) tan θ/(1+tan θ)=1, when θ=π/2.
As a result, π/2 times the output from the low-pass filter 107 becomes the approximate value of the phase. FIG. 33 shows a relationship between the phase of the input signal to the conventional phase detecting circuit and the detected phase.
FIG. 34 shows waveforms of output signals from the sections of the conventional phase detecting circuit obtained based on a simulation carried out by the computer. In FIG. 34, the horizontal axis shows time, and the unit of the numbers on the horizontal axis is cycle. In FIG. 34, (a) shows the phase of the received baseband signal; (b) shows the in-phase component and the quadrature component of the received baseband signal; (c) shows the output from the rotation projector 102; (d) shows the output from the integrator 103; (e) shows the output from the one-bit quantizer 104; (f) shows the output from the quadrant deciding section 101; (g) shows the output from the adder 106; and (h) shows the output from the low-pass filter 107. As is clear from FIG. 34, the output from the low-pass filter 107 shown in (h) is the result of quantizing the phase of the received baseband signal shown in (a).
The above shows the structure that the reception complex base band signal is directly input to the phase detecting circuit. However, instead of this method, it may be arranged as follows. The received baseband signal is rotated by a certain angle. The phase detecting circuit detects the phase of the signal after the rotation, and obtains the phase of the original received baseband signal by subtracting the phase of the rotated angle from this phase. For example, when the complex base band signal I+jQ is rotated by 45 degrees, and the resultant signal is multiplied by √2, it is possible to express this signal as shown by the equation (12).√{square root over (2)}ejπ/4(I+jQ)=(I−Q)+j(I+Q)  (12)
Therefore, it is possible to obtain the phase of the received baseband signal in the following order. Signals I−Q, and I+Q are prepared based on the received baseband signal I and Q. The signals I−Q, and I+Q are input to the phase detecting circuit. The phase detecting circuit detects the phases of these signals, and subtracts the quantized value corresponding to 45 degrees from the detected phases.
However, according to the conventional phase detecting circuit shown in FIG. 30, when the position of the received signal changes from the fourth quadrant to the first quadrant, for example, the output from the adder 106 of the conventional phase detecting circuit changes from “3 or 4” to “0 or 1”. Therefore, the output from the low-pass filter 107 becomes the intermediate value of around 2, which is a large deviation from around 0 or 4 as a correct phase. As explained above, the conventional phase detecting circuit disregards the cyclicity of the phase, and simply adds the phases. Consequently, there has been a problem that when the phase of the received signal changes by crossing over 0 or 2π, the phase of the signal output from the low-pass filter 107 is not correct (for example, at portion A in (h) in FIG. 34).
The conventional phase detecting circuit has another problem. Let us think of an example that the position of the received baseband signal I+jQ changes from the first quadrant to the second quadrant. The rotation projector 102 outputs −I (a negative value) or Q (a positive value) when the received signal is in the first quadrant. However, when the received signal enters the second quadrant, the rotation projector 102 outputs −Q (a negative value) or I (a positive value). At a position near the boundary between the first quadrant and the second quadrant, the absolute value of I is close to zero, but the absolute value of Q is not small. Therefore, the output from the rotation projector 102 changes based on the data output from the delay device 105. When the delay device 105 outputs 0, the signal Q in the first quadrant changes to −I in the second quadrant. When the delay device 105 outputs 1, the signal −I in the first quadrant changes to −Q in the second quadrant. Thus, there is a large change (for example, at portion B in (c) in FIG. 34). As explained above, the conventional phase detecting circuit has a problem that when the quadrant to which the received signal belongs changes, the output from the rotation projector 102 suddenly changes discontinuously, and a temporary error occurs in the phase detection value (for example, at portion C in (h) in FIG. 34).
Further, the analog FM receiver that uses the conventional phase detecting circuit has a problem that distortion rate characteristic of the demodulation signal becomes degraded, as the phase detection value becomes inaccurate because of the above two problems. Further, the FSK receiver and the PSK receiver that use the conventional phase detecting circuit have a problem that the reception bit error rate characteristic becomes degraded, for similar reasons.
Therefore, it is an object of the present invention to provide a phase detecting circuit that can realize accurate phase detection.